Quantum thermodynamics -- Bridging the gap between resource theories and the theory of open quantum systems

热力学理论告诉我们一些关于自然界基本极限的知识。它预测了时间箭头，并允许通过一些参数来理解复杂的机器。推导和理解小而强波动量子引擎的热力学定律是当今最重要和最迷人的研究方向之一。目前，量子热力学有两个看似无关的研究方向。一方面，人们遵循开放量子系统理论的传统来研究小量子系统在其环境影响下的动力学（例如，温度T下的热浴或外部激光场）。然后，利用统计力学的论据，在一定条件下，就有可能导出热力学定律，这些定律甚至对任意远离平衡态的强涨落系统也成立。这些预测中的许多也得到了实验验证。另一方面，在所谓的“资源理论”方法中，人们不从详细的微观描述开始，而是研究满足基本物理原理的特定变换（例如，节能）。给定这组转换，然后研究某些资源如何可以彼此转换（例如，有多少热量可以转化为功，或者哪些非平衡态可以转化）。不幸的是，由此产生的框架，它使用了许多来自量子信息理论的见解，是非常抽象的，很难在实验上实现。目前尚不清楚第一种方法中使用的假设是否与第二种方法兼容，反之亦然。到目前为止，这两种理论之间还没有富有成效的联系，本项目旨在缩小这一差距。本文主要探讨两个问题。首先，资源理论的假设有多现实，它们能在实验中实现吗？有没有可能将它们转化为开放量子系统理论？第二，在回答了第一个问题之后，我们是否可以利用资源理论研究的见解来了解更多关于开放量子系统的热力学？

The theory of thermodynamics teaches us something about the fundamental limits of nature. It predicts an arrow of time and allows to understand complicated machines in terms of a few parameters. Deriving and understanding the laws of thermodynamics for small and strongly fluctuating quantum engines presents one of the most important and fascinating research directions nowadays. At the moment there are two seemingly unrelated research directions in quantum thermodynamics. On the one hand, one follows the tradition of open quantum system theory to study the dynamics of a small quantum system under the influence of its environment (e.g., a heat bath at temperature T or an external laser field). Then, using arguments from statistical mechanics, it is possible under certain conditions to derive the laws of thermodynamics which hold even for strongly fluctuating systems arbitrarily far away from equilibrium. Many of these predictions have been also experimentally verified. On the other hand, within the so-called "resource theory" approach one does not start with a detailed microscopic description, but one rather studies specific transformations which fulfill elementary physical principles (e.g., energy conservation). Given this set of transformations one then studies how certain resources can be converted into each other (e.g., how much heat can be converted into work or which nonequilibrium states can be transformed). Unfortunately, the resulting framework, which uses many insights from quantum information theory, is very abstract and hard to implement experimentally. At present it is unclear as to whether the assumptions used in the first approach are compatible with the second approach and vice versa. There is no fruitful link between both theories so far and this project aims at closing this gap. It aims at exploring mainly two questions. First, how realistic are the assumptions of resource theories, can they be fulfilled in experiments and is it possible to translate them into the context of open quantum system theory? Second, after having answered the first question, can we use the insights from resource theoretic studies to learn more about the thermodynamics of open quantum systems?